Package org.drip.specialfunction.group

Class SchwarzTriangleMap

java.lang.Object

org.drip.specialfunction.group.SchwarzTriangleMap

public class SchwarzTriangleMap
extends java.lang.Object

SchwarzTriangleMap contains the Ratio of the Linearly Independent Solution pair corresponding to a given Singularity of the Hyper-geometric 2F1 Function. The References are:

• Gessel, I., and D. Stanton (1982): Strange Evaluations of Hyper-geometric Series SIAM Journal on Mathematical Analysis 13 (2) 295-308
• Koepf, W (1995): Algorithms for m-fold Hyper-geometric Summation Journal of Symbolic Computation 20 (4) 399-417
• Lavoie, J. L., F. Grondin, and A. K. Rathie (1996): Generalization of Whipple’s Theorem on the Sum of a (_2^3)F(a,b;c;z) Journal of Computational and Applied Mathematics 72 293-300
• National Institute of Standards and Technology (2019): Hyper-geometric Function https://dlmf.nist.gov/15
• Wikipedia (2019): Hyper-geometric Function https://en.wikipedia.org/wiki/Hypergeometric_function

It provides the following functionality:

• SchwarzTriangleMap Constructor
• Retrieve the Singularity
• Retrieve the Singularity Solution 0
• Retrieve the Singularity Solution 1
• Retrieve the Singularity Asymptote Order Term
• Retrieve the Connection Coefficient
• Indicate if the Triangle Map is Conformal
• Generate the s-Function corresponding to the Singularity Solution Pair
• Generate the Schwarz-Christoffel Triangle Vertex

Module	Computational Core Module
Library	Function Analysis Library
Project	Special Function Implementation and Analysis
Package	Special Function Singularity Solution Group

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
SchwarzTriangleMap(double singularity, R1ToR1 singularitySolution0, R1ToR1 singularitySolution1, R1ToR1 singularityAsymptoteOrderTerm, double connectionCoefficient)	SchwarzTriangleMap Constructor

Method Summary

Modifier and Type	Method	Description
double	connectionCoefficient()	Retrieve the Connection Coefficient
boolean	isConformal()	Indicate if the Triangle Map is Conformal
SchwarzChristoffelVertex	schwarzChristoffelVertex()	Generate the Schwarz-Christoffel Triangle Vertex
R1ToR1	sFunction()	Generate the s-Function corresponding to the Singularity Solution Pair
double	singularity()	Retrieve the Singularity
R1ToR1	singularityAsymptoteOrderTerm()	Retrieve the Singularity Asymptote Order Term
R1ToR1	singularitySolution0()	Retrieve the Singularity Solution 0
R1ToR1	singularitySolution1()	Retrieve the Singularity Solution 1

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

SchwarzTriangleMap

public SchwarzTriangleMap(double singularity,
R1ToR1 singularitySolution0,
R1ToR1 singularitySolution1,
R1ToR1 singularityAsymptoteOrderTerm,
double connectionCoefficient)
                   throws java.lang.Exception

SchwarzTriangleMap Constructor

Parameters:

singularity - The Singularity

singularitySolution0 - The Singularity Solution 0

singularitySolution1 - The Singularity Solution 1

singularityAsymptoteOrderTerm - The Singularity Asymptote Order Term

connectionCoefficient - The Connection Coefficient

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

singularity

public double singularity()

Retrieve the Singularity

Returns:

The Singularity

singularitySolution0

public R1ToR1 singularitySolution0()

Retrieve the Singularity Solution 0

Returns:

The Singularity Solution 0

singularitySolution1

public R1ToR1 singularitySolution1()

Retrieve the Singularity Solution 1

Returns:

The Singularity Solution 1

singularityAsymptoteOrderTerm

public R1ToR1 singularityAsymptoteOrderTerm()

Retrieve the Singularity Asymptote Order Term

Returns:

The Singularity Asymptote Order Term

connectionCoefficient

public double connectionCoefficient()

Retrieve the Connection Coefficient

Returns:

The Connection Coefficient

isConformal

public boolean isConformal()

Indicate if the Triangle Map is Conformal

Returns:

TRUE - The Triangle Map is Conformal

sFunction

public R1ToR1 sFunction()

Generate the s-Function corresponding to the Singularity Solution Pair

Returns:

The s-Function corresponding to the Singularity Solution Pair

schwarzChristoffelVertex

public SchwarzChristoffelVertex schwarzChristoffelVertex()

Generate the Schwarz-Christoffel Triangle Vertex

Returns:

The Schwarz-Christoffel Triangle Vertex